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Simplifying (4x + 1)(x + -3) = 9 Reorder the terms: (1 + 4x)(x + -3) = 9 Reorder the terms: (1 + 4x)(-3 + x) = 9 Multiply (1 + 4x) * (-3 + x) (1(-3 + x) + 4x * (-3 + x)) = 9 ((-3 * 1 + x * 1) + 4x * (-3 + x)) = 9 ((-3 + 1x) + 4x * (-3 + x)) = 9 (-3 + 1x + (-3 * 4x + x * 4x)) = 9 (-3 + 1x + (-12x + 4x2)) = 9 Combine like terms: 1x + -12x = -11x (-3 + -11x + 4x2) = 9 Solving -3 + -11x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -3 + -9 + -11x + 4x2 = 9 + -9 Combine like terms: -3 + -9 = -12 -12 + -11x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -12 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + -2.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.75x + x2 = 0 + 3 -2.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.75x + x2 = 3 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 3 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 3 + 1.890625 Combine like terms: 3 + 1.890625 = 4.890625 1.890625 + -2.75x + x2 = 4.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + -1.375) equal to 2.211475752 and -2.211475752.Subproblem 1
x + -1.375 = 2.211475752 Simplifying x + -1.375 = 2.211475752 Reorder the terms: -1.375 + x = 2.211475752 Solving -1.375 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.211475752 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.211475752 + 1.375 x = 2.211475752 + 1.375 Combine like terms: 2.211475752 + 1.375 = 3.586475752 x = 3.586475752 Simplifying x = 3.586475752Subproblem 2
x + -1.375 = -2.211475752 Simplifying x + -1.375 = -2.211475752 Reorder the terms: -1.375 + x = -2.211475752 Solving -1.375 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.211475752 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.211475752 + 1.375 x = -2.211475752 + 1.375 Combine like terms: -2.211475752 + 1.375 = -0.836475752 x = -0.836475752 Simplifying x = -0.836475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.586475752, -0.836475752}
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